Walker, Halliday & Resnick — Temperature, Heat, and the First Law of Thermodynamics: Problem 31

31 Ice has formed on a shallow pond, and a steady state has been reached, with the air above the ice at \(-5.0^\circ\text{C}\) and the bottom of the pond at \(4.0^\circ\text{C}\). If the total depth of ice + water is \(2.0\text{ m}\), how thick is the ice? (Assume that the thermal conductivities of ice and water are \(0.40\) and \(0.12\text{ cal/m} \cdot \text{C}^\circ \cdot \text{s}\), respectively.)